o µ ] } v W z x I s F t F x · 2020. 3. 16. · ^ } o µ ] } v W A B y F t F u s r w z r s C U A B...
Transcript of o µ ] } v W z x I s F t F x · 2020. 3. 16. · ^ } o µ ] } v W A B y F t F u s r w z r s C U A B...
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Solution:
A = 7 −2 −3 10
5 80 1
, B = 8 −1 4 −2
, C =
−6 30 49 −28 5
, D = 5 −32 0
86
1 −2 −6
a) A2 x 4, B2 x 2; number of columns of A (4) is not equal number of rows of B (2). Therefore, AB does not exist.
b) AT =
7 −3−2 105 08 1
, ATB =
7 −3−2 105 08 1
8 −1 4 −2
=
⎣⎢⎢⎡7 ∗ 8 + (−3) ∗ (4) 7 ∗ (−1) + (−3) ∗ (−2)
−2 ∗ 8 + 10 ∗ 4 −2 ∗ (−1) + 10 ∗ (−2)
5 ∗ 8 + 0 ∗ 4 5 ∗ (−1) + 0 ∗ (−2)
8 ∗ 8 + 1 ∗ 4 8 ∗ (−1) + 1 ∗ (−2) ⎦⎥⎥⎤
=
44 −124 −1840 −568 −10
.
c) AC= 7 −2 −3 10
5 80 1
−6 30 49 −28 5
=
7 ∗ (−6) + (−2) ∗ 0 + 5 ∗ 9 + 8 ∗ 8 7 ∗ 3 + (−2) ∗ 4 + 5 ∗ (−2) + 8 ∗ 5
(−3) ∗ (−6) + 10 ∗ 0 + 0 ∗ 9 + 1 ∗ 8 (−3) ∗ (3) + 10 ∗ 4 + 0 ∗ (−2) + 1 ∗ 5 =
=67 43 26 36
d) 2B +3I2 = 2 8 −1 4 −2
+3 1 0 0 1
= 2 ∗ 8 + 3 ∗ 1 2 ∗ (−1) + 0 2 ∗ 4 + 3 ∗ 0 2 ∗ (−2) + 3 ∗ 1
= 19 −2 8 −1
e) det 5 −32 0
86
1 −2 −6=
5 −32 0
86
1 −2 −6
5 −32 01 −2
= 5*0*(-6)+(-3)*6*1+8*2*(-2) – 8*0*1- 5*6*(-2)–(-3)*2*(-6) = -26.
f) det 8 −1 4 −2
= 8 ∗ (−2) − (−1) ∗ 4 = −12.
B-1 = 1/(-12) −2 1 −4 8
= 1/6 −1/12 1/3 −2/3
.